REML estimation;



Model descriptionRestricted maximum likelihood estimation (REML) is often used to estimate variance parameters in the linear mixedmodel:
y = X*b + Z*u + e
where X and Z are covariate matrices, b are the fixedeffects, u are the
random effects and e are the error terms. One way of defining the REML procedure is to:
To implement this in ADMBRE we declare both b and u as random effects vectors. As a result, the likelihood is integrated with respect to both parameters. But, while there is a contribution to the objective function comming from the random effects distribution of u, there should be no such contribution from b (i.e. a flat prior). Using this procedure you do not have to derive the "REML correction" to the loglikelihood function by hand. It is done automatically for you by ADMBRE. Example: BCB BowheadsPunt and Zeh (2004, document SC/56/BRG1 presented to the SC of the IWC) combined data from two different counting methodologies in order to estimate the rate of increase of BCB bowhead whales. On a logscale they fitted a linear mixedeffects models using REML estimates for the variance parameters. This example (bcb.tpl) shows how random_effects can be used to obtain REML estimates.
